The Fire scored first in the eighth minute when Cuauhtemoc Blanco looped a pass over the top of the Crew defense to midfielder Justin Mapp, who fired a shot off the left post. Rolfe scored on the rebound.
Chicago doubled its lead in the 25th minute when Calen Carr drove the ball past Will Hesmer for his second goal of the season.
The Crew cut the gap to 2-1 nine minutes before the first-half break when Emmanuel Ekpo put a shot over Jon Busch from in close. The final, and tying goal, came in the 87th minute when late substitute Steven Lenhart scored.
The Crew (8-4-3) are just three points behind the league-leading New England Revolution in the Eastern Conference. Chicago (6-5-3) is nine points back of the leaders.